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arXiv · 2610.04501

Multiple solutions of singular periodic problems

Milan Tvrdý
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Abstract

In this contribution we consider the singular periodic problem \[ u''+k\,u=g(u)+e(t),\quad u(0)=u(2π),\,\,u'(0)=u'(2π), \] where $k\in\R,$ $e:\J\to\R$ is Lebesgue integrable and $g:\I\mapsto\R$ is continuous, but can have a singularity at $x=0.$ In particular, I wish to revisit our earlier result regarding the existence of at least two its solutions and present a proof that is somewhat more transparent than the original one.

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Milan Tvrdý. 2026-10-03. Multiple solutions of singular periodic problems. https://arxiv.org/abs/2610.04501

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